Simulation and analysis of industrial crystallization processes through multidimensional population balance equations. Part 1: a resolution algorithm based on the method of classes

Abstract

In order to obtain constant solid properties with particles exhibiting a low order of symmetry, it is necessary to monitor and to control several distributed parameters characterising the crystal shape and size. A bi-dimensional population balance model was developed to simulate the time variations of two characteristic sizes of crystals. The nonlinear population balance equations were solved numerically over the bi-dimensional size domain using the so-called method of classes. An effort was made to improve usual simulation studies through the introduction of physical knowledge in the kinetic laws involved during nucleation and growth phenomena of complex organic products. The performances of the simulation algorithm were successfully assessed through the reproduction of two well-known theoretical and experimental features of ideal continuous crystallization processes: the computation of size-independent growth rates from the plot of the steady-state crystal size distribution and the possibility for MSMPR crystallizers to exhibit low-frequency oscillatory behaviours in the case of insufficient secondary nucleation.